Geometric nelder-mead algorithm on the space of genetic programs

@InProceedings{Moraglio:2011:GECCO,
author = "Alberto Moraglio and Sara Silva",
title = "Geometric nelder-mead algorithm on the space of
genetic programs",
booktitle = "GECCO '11: Proceedings of the 13th annual conference
on Genetic and evolutionary computation",
year = "2011",
editor = "Natalio Krasnogor and Pier Luca Lanzi and
Andries Engelbrecht and David Pelta and Carlos Gershenson and
Giovanni Squillero and Alex Freitas and
Marylyn Ritchie and Mike Preuss and Christian Gagne and
Yew Soon Ong and Guenther Raidl and Marcus Gallager and
Jose Lozano and Carlos Coello-Coello and Dario Landa Silva and
Nikolaus Hansen and Silja Meyer-Nieberg and
Jim Smith and Gus Eiben and Ester Bernado-Mansilla and
Will Browne and Lee Spector and Tina Yu and Jeff Clune and
Greg Hornby and Man-Leung Wong and Pierre Collet and
Steve Gustafson and Jean-Paul Watson and
Moshe Sipper and Simon Poulding and Gabriela Ochoa and
Marc Schoenauer and Carsten Witt and Anne Auger",
isbn13 = "978-1-4503-0557-0",
pages = "1307--1314",
keywords = "genetic algorithms, genetic programming",
month = "12-16 " # jul,
organisation = "SIGEVO",
address = "Dublin, Ireland",
DOI = "doi:10.1145/2001576.2001753",
publisher = "ACM",
publisher_address = "New York, NY, USA",
abstract = "The Nelder-Mead Algorithm (NMA) is a close relative of
Particle Swarm Optimization (PSO) and Differential
Evolution (DE). In recent work, PSO, DE and NMA have
been generalized using a formal geometric framework
that treats solution representations in a uniform way.
These formal algorithms can be used as templates to
derive rigorously specific PSO, DE and NMA for both
continuous and combinatorial spaces retaining the same
geometric interpretation of the search dynamics of the
original algorithms across representations. In previous
work, a geometric NMA has been derived for the binary
string representation and permutation representation.
Furthermore, PSO and DE have already been derived for
the space of genetic programs. In this paper, we
continue this line of research and derive formally a
specific NMA for the space of genetic programs. The
result is a Nelder-Mead Algorithm searching the space
of genetic programs by acting directly on their tree
representation. We present initial experimental results
for the new algorithm. The challenge tackled in the
present work compared with earlier work is that the
pair NMA and genetic programs is the most complex
considered so far. This combination raises a number of
issues and casts light on how algorithmic features can
interact with representation features to give rise to a
highly peculiar search behaviour.",
notes = "Also known as \cite{2001753} GECCO-2011 A joint
meeting of the twentieth international conference on
genetic algorithms (ICGA-2011) and the sixteenth annual
genetic programming conference (GP-2011)",
}